Jane owns an apple strudel bakery shop in Katong area. She sells each roll of apple strudel for $10. Her cost is $6 per roll of apple strudel, giving her a $4 profit on each roll of apple strudel sold. From the historical daily demand data, Jane noticed the following trend: 20% of the time daily demand is 100 rolls 20% of the time daily demand is 150 rolls 30% of the time daily demand is 200 rolls 30% of the time daily demand is 250 rolls A lost sale occurs when the daily demand exceeds the number of rolls baked daily and this will incur a cost of $1 for every roll lost sale due to loss of goodwill. On the other hand, any unsold rolls each day will be thrown away. (a) Identify the probability distribution table of past daily demand with the header "Daily Demand" and "Probability". (b) Identify the corresponding interval of random numbers (in decimals) for "Daily Demand" using the probability information derived in Part (a). (c) Using the interval in Part (b), simulate the daily demand for the next 5 days based on the five random number sequence: 0.52, 0.07, 0.50, 0.86, 0.61. (d) Using the result in Part (c), simulate Jane's profit outlook over the 5 days if Jane decides to bake only 180 rolls per day. Interpret the simulation result and calculate the total profit for the 5-day period